Amorphous-amorphous transition in glassy polymers subjected to cold rolling studied by means of positron annihilation lifetime spectroscopy

Amorphous-amorphous transition in glassy polymers subjected to cold

rolling studied by means of positron annihilation lifetime spectroscopy

D. Cangialosia兲

Department of Polymer Materials and Engineering, Delft University of Technology, Julianalaan 136, 2628 BL Delft, The Netherlands and Dutch Polymer Institute, P.O. Box 902, 5600 AX Eindhoven, The Netherlands

M. Wübbenhorst

Department of Polymer Materials and Engineering, Delft University of Technology, Julianalaan 136, 2628 BL Delft, The Netherlands

H. Schut and A. van Veenb兲

Interfaculty Reactor Institute, Delft University of Technology, Mekelweg 15, 2629 JB Delft, The Netherlands S. J. Picken

Department of Polymer Materials and Engineering, Delft University of Technology, Julianalaan 136, 2628 BL Delft, The Netherlands and Dutch Polymer Institute, P.O. Box 902, 5600 AX Eindhoven, The Netherlands

共Received 7 June 2004; accepted 9 November 2004; published online 26 January 2005兲

In this study, polycarbonate 共PC兲 and polystyrene 共PS兲 are subjected to plastic deformation by means of cold rolling and the resulting variation of the free volume and its subsequent time evolution after rolling is investigated by means of positron annihilation lifetime spectroscopy 共PALS兲. The value of the long lifetime component that is attributed to the decay of ortho-positronium共␶_o-Ps兲 and its intensity 共I_o-Ps兲 are used to characterize, respectively, the size and the concentration of the free-volume holes. In addition to the PALS experiments, the effect of plastic deformation on the dynamic tensile modulus is investigated. The PALS results show that both for well-aged PC and PS an increase of␶_o-Ps and a decrease of I_o-Ps occur upon plastic deformation. During the subsequent aging,␶_o-Pstends to return to the value assumed before plastic deformation, while I_o-Ps remains constant with time. These results corroborate the idea of an amorphous-amorphous transition, rather than that of a “mechanical rejuvenation” as proposed in the past to explain the ability of plastic deformation to reinitiate physical aging. Finally, a linear relation between the size of the free-volume holes and the dynamic tensile modulus is found, which suggests that the stiffness of amorphous glassy polymers is fully determined by their nanoscopic structure. © 2005 American Institute of Physics.关DOI: 10.1063/1.1844396兴

I. INTRODUCTION

The physics of the glassy state has been the subject of a number of studies throughout the past decades. In particular, great interest has been devoted to the slow evolution of the thermodynamic properties that occurs after cooling from the equilibrium melt. Increasing relaxation times result from a temperature reduction and the glass former cannot equili-brate during the time scale of feasible experiments. The structural changes introduced by this phenomenon, known as “physical aging,” can be erased by increasing the tempera-ture above the glass transition of the glass former. This effect is generally known as “thermal rejuvenation.”1 However, it was also proposed that application of large stresses in the glassy state can have the same effect of erasure of the ther-momechanical history of the sample.1,2In this case, a “me-chanically rejuvenated” glass is obtained with properties re-sembling those of a thermally rejuvenated glass.

Recently, McKenna,3 discussing a number of experi-ments performed on materials stressed above the yield point, showed that polymeric glasses seem to end up into a new state, which is different from the one obtained after thermal rejuvenation above T_g. In particular, he showed that the ap-plication of stresses above the yield point generates a calori-metric response in the neighborhood of T_g, which is different from that of thermally rejuvenated samples. Similar to the case of thermal rejuvenation, the exothermic peak appearing in the enthalpy-temperature plot after aging disappears after mechanical rejuvenation. However, in the latter case a sub-glass transition minimum in the enthalpy appears. In addi-tion, the decrease over time of the yield stress after thermal and mechanical rejuvenation differs greatly, particularly in the equilibrium values of the yield stress.4 Based on these observations, it was proposed that application of large stresses may lead to a sort of amorphous-amorphous transition.3Theoretically, this idea is supported by the con-cept of the “potential energy landscape.”5Using this concept, Malandro and Lacks6and Gagnon et al.7describe yielding as the promotion of mechanical instabilities by means of

mo-a兲_{Present address: Fundacion Donostia International Physics Center, Paseo} Manuel de Lardizabal, 4-20018 San Sebastian, Spain.

b兲_Deceased.

lecular simulation on particles interacting through the Weber and Stillinger potential.8This, in turn, drives the system to a different potential energy minimum. Monte Carlo simulation applied to plastically deformed silica, shows such a jump to a different potential energy minimum, which in this case is explained by a continuous increase of the coordination num-ber from four to six.9,10 More evidence for a pressure in-duced amorphous-amorphous transition in a number of non-polymeric glasses is reported in a recent review.11By means of atomistic modeling, Jang and Jo12corroborate the idea of an amorphous-amorphous transition in the case of polymers. They showed that the ratio of trans/gauche/unstable state of the dihedral angles in poly共trimethylene terephthalate兲 under-goes a substantial change upon stress application.

Interesting results have also been obtained from density measurements. In particular, a number of studies have been reported in the past on cold rolled polycarbonate 共PC兲 and acrylonitrile-butadiene-styrene copolymer,13 and more re-cently on polystyrene共PS兲.14These studies show an increase or very little changes of the density of the polymers after rolling instead of the expected decrease for a rejuvenated sample.

Though the macroscopic effects induced by the applica-tion of large stresses are quite well understood in terms of mechanical and thermodynamic properties, a clear interpre-tation of these results from a microscopic point of view is still lacking. The purpose of this study is to clarify this aspect by means of positron annihilation lifetime spectroscopy 共PALS兲, which allows the characterization of the free-volume structure of polymers. In this technique, positrons emitted by a radioactive source 共22Na兲 are injected into the polymer where they annihilate. Apart from direct annihila-tion, positrons can also pick up an electron before annihilat-ing and form ortho-positronium 共o-Ps兲 or para-positronium 共p-Ps兲. The latter has a very short lifetime 共125 ps in vacuum兲 and is not useful to characterize the free volume of polymers. On the other hand, o-Ps has a lifetime in vacuum of 140 ns that is strongly reduced in polymers to few nano-seconds depending on the free-volume properties of the sample.15 In particular, the measured o-Ps lifetime is related to the size of the free-volume cavity using the following semiempirical equation:16 ␶o-Ps= 1 2

冋

冉

冊

册

where R is the radius of the cavity. Equation共1兲 describes the o-Ps lifetime and, although derived for an infinitely deep potential well共representing the assumed spherical cavity兲, it contains the empirical parameter ⌬R=1.656 Å that allows the overlap between the positron and the electron wave func-tion, which would otherwise not be possible due to the infin-ity of the potential well.16

The intensity of o-Ps共Io-Ps兲, which is proportional to the

probability of positronium formation, has been related in the past to the density of free-volume holes in the polymer.17 However, it was found that Io-Ps is also affected by the

chemical composition of the polymer,18 the source strength and electrostatic charging due to prolonged irradiation,19–21 electric fields22,23and visible light.24 Although the

interpre-tation of I_o-Ps as a measure for free volume has been questioned,25we believe that, provided that all the previously mentioned effects are carefully eliminated, or at least mini-mized, a direct relation between Io-Ps and the hole density

exists. In the present study, we compare the free-volume pa-rameters of systems with共i兲 exactly the same chemical com-position; 共ii兲 no charging or visible light effects; 共iii兲 where the same source has been used for all the experiments; and 共iv兲 where only one sample is used for each experiment to avoid accumulation of charges. Under similar experimental conditions, it was shown in the past that the reduction of Io-Ps

during physical aging of PC, gives useful information on the evolution of the polymer structure.26,27 For this reason, we feel that it is justified to use the following equation to evalu-ate the variation the free-volume percentage compared to “fresh” samples 共in this case before plastic deformation兲:

冉

冊

where the subscript共0兲 indicates the free-volume properties of the fresh samples, V_totis the overall volume, and A is an empirical parameter taken from literature data. The value of

R is derived from the lifetime using Eq. 共1兲. Although for

large variations of hole density Eq. 共2兲 is not rigorously valid,17 we assume a linear relation between the concentra-tion of holes and Io-Pssince the variation of Io-Psis small, as

it will be seen in the results section. Note that in Eq.共2兲 the variation of the overall volume was assumed to be negligible compared to the variation of the free volume. For a free-volume percentage of about 7% and variation of less than 1%, this results in a negligible error.

The free-volume properties as determined by PALS of plastically deformed polymers were studied in the past by Hasan et al.28 However, the PALS parameters were deter-mined during plastic deformation and no hint of a new struc-ture obtained in this manner was reported. To the best of our knowledge, no studies exist on the microscopic structure as-sumed by glassy amorphous polymers after plastic deforma-tion. The purpose of this paper is to determine the micro-scopic free-volume structure of “mechanically rejuvenated” PC and PS by means of cold rolling and to interpret the results in terms of polymorphism of the glassy state of poly-mers. The PALS results are supported by dynamic-mechanical tests in order to further investigate possible links between free volume and macroscopic mechanical proper-ties.

II. EXPERIMENT

A. Materials and sample preparation

The materials used in this study are a commercial grade PC共Lexan 161兲 from General Electric Co. and a commercial grade PS 共Styron 648兲 from Dow Chemical with Mw

= 318 490 and polydispersity of 3.09.

Cold rolling was carried out on 3.2 mm thick PS and PC using a two-roller mill. “Well-aged” injection moulded

samples were employed for the rolling. The thickness reduc-tions investigated in this study were 19%, 28%, 33%, and 41% for PC, and 20%, 29%, 35%, and 40% for PS. It is worth remarking that, for all thickness reductions, all of the samples pass the yield point and reach the plastic deforma-tion region. Samples of about 1 cm2 _{were used for PALS}

measurements, whereas tensile bars according to ASTM D 638 were used for dynamic tensile modulus measurements.

B. PALS measurements

PALS measurements were performed at room tempera-ture using radioactive 22NaCl source with an activity of 10␮Ci. The duration of each experiment was about 8 h, which is low enough to minimize charging effects. This was recently demonstrated for PC,21 while for PS we have per-formed preliminary experiments that also show negligible charging effects in the time scale of several hours.

Details on the experimental setup are given in a previous paper.26The positron lifetime spectrum y共t兲 is analyzed using the programPOSITRONFIT, which describes the spectrum as a convolution of the instrument resolution function and a finite number of decaying exponentials plus the background as de-scribed by the following equation:29

y共t兲 = R共t兲丢

冉

兺

i=1 n

Ii␭iexp共− ␭it兲 + B

冊

Here R共t兲 is the resolution function of the system, ␭i is the

annihilation rate共inverse of the lifetime component ␶_i兲, and

B is the background signal. All spectra were resolved in three

lifetime components: a short one systematically larger than the lifetime in vacuum of p-Ps共125 ps兲, in agreement with recent studies on delayed positronium formation,30 an inter-mediate one of around 400 ps related to free positron anni-hilation, and a long component共␶o-Ps兲 related to o-Ps

annihi-lation. The ratio of the intensities of p-Ps and o-Ps was systematically higher than the commonly accepted value 共1/3兲. This was also shown to be the case in Ref. 30.

C. Mechanical characterization

Tensile samples, according to ASTM D638, were cold rolled to a thickness reduction of 10% for PC and 30% for PS. Immediately after rolling the specimen was mounted in a MTS 831 servo-hydraulic tensile tester. The dynamic modu-lus was subsequently measured using a sinusoidal excitation at a frequency of 1 Hz with an amplitude of 0.2% strain. To avoid buckling the sample was prestrained by 0.3%. The modulus determined was averaged over 20 cycles. After this measurement the sample was unloaded and left undisturbed for a certain period of time. Subsequently the modulus mea-surement was repeated followed again by unloading and a period of undisturbed aging. In this way the evolution of the dynamic tensile modulus was monitored stepwise over a pe-riod of⬇15 h.

III. RESULTS

In Figs. 1, 2共a兲, and 2共b兲, the effect of the thickness reduction just after cold rolling on␶o-Ps and Io-Ps is plotted,

respectively, for PC and PS. The following observations are made by analyzing the figures:

共i兲 Both␶o-Psand Io-Psundergo a significant change upon

cold rolling in the plastic deformation region. In particular, ␶o-Psincreases, whereas a reduction of Io-Pscan be observed. 共ii兲 No significant dependence of the PALS parameters on the thickness reduction appears, provided that the samples are rolled above the yield point as done in this study.

共iii兲 PC and PS show a similar trend.

Figures 1 and 2共c兲 show the variation of the free-volume percentage obtained using Eq.共2兲, with A=0.002 26 Å−3_for

PC and A = 0.001 27 Å−3 _{for PS. These values are derived}

from the extrapolation of literature data.31As it can be seen A is a material specific parameter, which depends on the chem-istry of positronium formation共availability of electrons兲. The

FIG. 1. Effect of the percentage of thickness reduction on the PALS param-eters of PC:共a兲␶o-Ps;共b兲 Io-Ps; and共c兲 variation of the free-volume percent-age. The dashed lines are a guide for the eye.

results indicate a free-volume change corresponding to a variation of the specific volume of about 0.2% for PC. For PS, the free volume seems to increase slightly, although the microstructure must have changed dramatically as shown by the behavior of␶o-Psand Io-Ps.

Beside the PALS results, the variation of the tensile modulus before and after cold rolling is shown in Table I. A clear decrease in the tensile modulus of PC and PS for a thickness reduction of, respectively, of 10% and 30% can be observed just after cold rolling.

The time dependence after cold rolling of both the PALS parameters and tensile modulus was also monitored. Figures 3, 4共a兲, and 4共b兲 show a progressive decrease of␶o-Ps, which

tends to return to the value before rolling both for PC and PS. On the other hand, the figures show a constant Io-Ps,

within the experimental uncertainty.

From the time evolution of␶_o-Ps and I_o-Ps, the variation of the free-volume percentage can be evaluated. As shown in Figs. 3 and 4共c兲, the free volume evolves towards smaller values than the ones just after rolling, due to the decrease in ␶o-Ps. In Figs. 3 and 4 we have referred the free-volume

variation to the value before rolling. It is worth noting that for PC a densification occurs on systems that have already undergone densification due to the cold rolling. In the case of PS, although cold rolling induces a slight increase in the free volume, the system evolves to a free volume smaller than the one before rolling, which, as pointed out in the Introduction, was not evolving in spite of the larger free volume 共“well aged”兲. This is, at least apparently, in contradiction with

FIG. 2. Effect of the percentage of thickness reduction on the PALS param-eters of PS:共a兲␶o-Ps;共b兲 Io-Ps; and共c兲 variation of the free-volume percent-age. The dashed lines are a guide for the eye.

TABLE I. Dynamic tensile moduli of PC and PS before and after cold rolling. Here the thickness reduction is 10% and 30% for PC and PS, re-spectively.

Polymer E⬘共MPa兲 before rolling E⬘共MPa兲 after rolling

PC 2660 2540

PS 3570 3475

FIG. 3. Time evolution after cold rolling of the PALS parameters of PC:共a兲

␶o-Ps;共b兲 Io-Ps; and共c兲 variation of the free-volume percentage referred to the state before plastic deformation. The dashed lines are a guide for the eye.

simple free-volume concepts, which relate mobility directly to the overall free volume in the system.1,2This point will be discussed in more detail in the following section of this paper.

For the tensile modulus, the same type of time evolution was obtained. Interestingly, the dynamic modulus follows a similar trend to␶o-Ps, i.e., it tends to return to its value before

rolling in the same time scale as␶o-Psas shown in Fig. 5. In

addition, as pointed out by Van Melick et al.,14 recovery of the yield stress and strain softening occurs with the same kinetics. In summary, although from the point of view of the mechanical properties, both PC and PS seem to return to their original state, before cold rolling, it is evident from PALS experiments that cold-rolled amorphous glassy poly-mers have a microstructure that is rather different from the original one.

IV. DISCUSSION

In the preceding section of the paper, the free volume of PC and PS after plastic deformation was evaluated by means

of PALS as a combination of size共␶_o-Ps兲 and concentration of holes共Io-Ps兲. In this way, we were able to show that plastic

deformation of well-aged PC and PS produces an increase in the size of the free-volume holes and a decrease of the con-centration of the holes. In previous studies, preformed by some of us on PC, it was shown that physical aging after thermal rejuvenation produces a reduction of the concentra-tion of free volume holes, while the cavity size remains unaltered.26,27 This means that a “true” rejuvenation of a well-aged sample should restore the structure to that present before the onset of physical aging, and should hence produce an increase in the concentration of free-volume holes, which means an increasing I_o-Pswhile no changes in␶_o-Pswould be expected. It is therefore a straightforward conclusion that, according to our present PALS results, amorphous glassy polymers after plastic deformation have a structure that is qualitatively different from that of a thermally rejuvenated sample. The idea of rejuvenation induced by mechanical de-formation as formulated by Struik1,2is clearly not supported by our PALS results. On the other hand, our results do sup-port the hypothesis of an amorphous-amorphous transition, as proposed by McKenna.3We believe that the rejuvenating effect of plastic deformation was misinterpreted due to its ability to reinitiate physical aging similar to thermal rejuve-nation. The main feature of the time evolution of the free volume after plastic deformation is the reduction of the cav-ity size, as testified by the reduction of the␶o-Psrather than

the reduction of the concentration of free-volume holes as is

FIG. 4. Time evolution after cold rolling of the PALS parameters of PS:共a兲

␶o-Ps;共b兲 Io-Ps; and共c兲 variation of the free-volume percentage referred to the state before plastic deformation. The dashed lines are a guide for the eye.

FIG. 5. Time evolution after cold rolling of the dynamic tensile modulus for

the case of physical aging after thermal rejuvenation.26,27In other words, although the macroscopic volume reduction is very similar in both cases, the microscopic mechanism for this free-volume reduction is totally different. In addition, another important observation of the effect produced by plas-tic deformation is the persistence of the change of the Io-Ps,

which can be considered as a signature of the new amor-phous state. From a potential energy landscape point of view,5the new minimum, which the glassy state enters dur-ing plastic deformation, corresponds to a situation with a smaller number of free-volume holes.

Our PALS results agree nicely with the change of den-sity reported for PC 共Ref. 13兲 and PS 共Ref. 14兲 after plastic deformation. In particular, Broutman and Patil13found a de-crease of the specific volume of 0.25% for PC and Van Melick et al.14 find a very slight decrease of PS specific volume共about 0.03%兲. Comparing these data with our PALS results in Figs. 1 and 2, it looks like our results show a smaller increase in density, since we find a free-volume de-crease of 0.2% for PC and even an inde-crease of 0.05% for PS. The change of the dynamic modulus after plastic defor-mation and its subsequent time evolution is also very inter-esting, especially when considering the size of the free-volume holes as probed by PALS. Recently, Schmidt et al.32 showed that a universal law holds relating the bulk modulus to the volume of the free-volume holes. In particular, the bulk moduli of a large number of polymers were found to decrease linearly with the cavity size. In other words, the macroscopic stiffness of the polymer was found to be related exclusively to the size of the free-volume holes. Although in this work we have employed the dynamic elongation modu-lus rather than the bulk modumodu-lus, a similar correlation was found. In fact, plastic deformation at the same time produces a reduction of the dynamic modulus and an increase of the size of the free-volume holes, i.e.,␶o-Ps, similar to the

find-ings of Schmidt et al.32 This is valid for both PC and PS. During the subsequent time evolution, the modulus increases and the ␶_o-Psdecreases within the same time scale. From a quantitative point of view, this is shown in Fig. 6 where the volume of the free-volume holes, calculated from␶o-Psusing

Eq. 共1兲, is plotted versus the dynamic modulus correspond-ing to the same time after plastic deformation. In agreement with Schmidt et al.32an inverse linear relation is obtained.

It is worth mentioning that in order to get hole volume and dynamic moduli at the same time after plastic deforma-tion, the experimental values of the latter were fitted through an exponential law, which was found to be suitable to de-scribe the time evolution of the dynamic moduli. This allows the dynamic moduli to be calculated at the same time after plastic deformation as in the PALS experiments.

Finally, we would like to comment on the interpretation of our PALS results. First of all it was assumed that Eq.共1兲, obtained under the assumption of spherical cavities,16 is valid even for nonspherical ones, which could in principle be present in samples subjected to plastic deformation via cold rolling. This procedure can induce orientation in the polymer sample, and could also give rise to the formation of non-spherical cavities. However, experimentally we have found that injection moulded amorphous polymer samples, which

were clearly oriented from the observed birefringence, did not show significant differences in the ␶o-Ps compared to

similar samples free of orientation. This means that Eq. 共1兲 probably is a good approximation even for nonspherical cavities, at least for the strains applied in the present situa-tion.

Another point for discussion is the structural significance of Io-Ps. Recently, it was observed that application of large

stresses to amorphous glassy polymers can lead to the mation of free radicals, which would inhibit positronium for-mation and, therefore, lead to a reduction in the Io-Ps.

33

How-ever, our experimental conditions are much less drastic than those as reported by Günther-Schade et al.33However, even if a certain amount of radicals are present, we believe that they do not affect Io-Psfor three reasons:

共i兲 Though we do not have any direct experimental evi-dence, we can postulate that the concentration of radicals should increase with the amount of deformation applied to the samples upon cold rolling and this would lead to a re-duction of Io-Psdependent on the plastic deformation. In our

case, I_o-Ps is independent of the plastic deformation, as shown in the Results section;

FIG. 6. Relation between the hole volume and the dynamic tensile modulus during the time evolution after cold rolling. The values of the dynamic tensile modulus are calculated from the exponential fitting of the experimen-tal values of the dynamic modulus with time. The dashed lines are a guide for the eye.

共ii兲 Though in the glassy state, radicals would slowly disappear with time and I_o-Ps would go up. That does not occur and, instead, I_o-Ps stays at the new value after cold rolling indefinitely;

共iii兲 As already discussed, the variation of the free vol-ume evaluated from both Io-Psand␶o-Psresembles the

varia-tion of the specific volume evaluated using macroscopic techniques.13,14

These observations support our interpretation of Io-Psas a

factor that provides significant information on the polymer structure, at least if the experimental procedures are carefully executed to avoid various possible artifacts.

V. CONCLUSIONS

The effect of plastic deformation induced by cold rolling of glassy PC and PS has been investigated by means of PALS and dynamic-mechanical spectroscopy, which yields information on the time dependent evolution of the free-volume microstructure and the dynamic moduli. An increase of the size of the free-volume holes and a decrease of their concentration is observed as a consequence of plastic defor-mation. The subsequent time evolution of the free-volume proceeds via a reduction of the size of the free-volume holes towards the value that occurred before plastic deformation, while the concentration of free-volume holes remained con-stant. These results indicate that plastic deformation pro-vokes an amorphous-amorphous transition in amorphous glassy polymers similar to the ones occurring in other glassy systems like silica. On the other hand, the idea of a mechani-cal rejuvenation, which arose from the experimental obser-vation of reinitiated physical aging, is not supported by our PALS results. In fact, the time evolution of the free volume after plastic deformation suggests a totally different micro-structure of the free volume compared to the micro-structure after thermal rejuvenation, which consists of the reduction of the concentration of free-volume holes. Finally, the dynamic modulus after plastic deformation and its subsequent time evolution shows a clear relation to the change in volume of the free-volume holes, indicating that the stiffness of amor-phous glassy polymers can be fully attributed to the free-volume structure as probed by PALS.

ACKNOWLEDGMENTS

The work of D.C. and S.J.P. forms part of the research program of the Dutch Polymer Institute共DPI兲. This work is carried out under DPI Project No. 285: “Influence of Applied Stress and Physical Ageing on Diffusion and Solubility of Oxygen and Anti-Oxidants.” The authors would like to thank

C. J. M. Meesters and L. E. Govaert of the department of Mechanical Engineering at Eindhoven University of Tech-nology for their assistance in the mechanical characterization of the rejuvenated samples.

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